| Spiral bevel gears have been widely applied in the aerospace,energy machinery and NC machine tools for motion and power transmission between intersecting axes,owing to their high contact ratio,strong load capacity and low noise.The developing trends of high precision,transmission efficiency and power density for gears have made higher demands on strength,meshing performance and transmission reliability.It is of great significance to predict the reliability and stability of gear by calculating the contact ratio,the load distribution,the transmission precision,the bending and the contact fatigue strength of the spiral bevel gear because of the complex tooth surface.The friction and installation error are inevitable during the meshing process of the gear.In this paper,the bending and contact stresses of spiral bevel gear in consideration of friction are calculated,and the effect of the installation error on the meshing characteristic of the gear is analyzed.The main contents are as follows:(1)Geometric modeling of spiral bevel gear.Equations of the tooth profile and pitch line of the gear are derived based on the principles of spherical involute forming and generating machining,respectively.The tooth surface equation is solved to acquire the discrete point data of the surface by MATLAB.The discrete points are used for curve and surface fitting to obtain the tooth surface on working,and the geometric model of spiral bevel gear is finally established by CATIA.(2)Finite element contact analysis of spiral bevel gear.Finite element model(FEM)of the gear is established based on ABAQUS and finite element contact theory,then the contact ratio,load distribution ratio,static transmission error,time-varying meshing stiffness,bending and contact stresses of spiral bevel gear are calculated to analyze the meshing characteristic of the gear.(3)Calculation of bending and contact stresses of spiral bevel gear in consideration of friction.Taking the pitch line as demarcation,friction distribution on the driving gear surface is analyzed,and the effect of friction on load distribution and static transmission error of the gear are investigated.Then the formulation of bending stress of the gear with friction is proposed according to Lewis cantilever model on the basis of ISO gear bending strength standard.Meanwhile,the formulation of contact stress under the normal force and friction is given by the Hertz contact and fourth strength theory based on ISO gear contact strength standard.Effects of friction on the bending and contact stresses of the tooth are further investigated,and the results are compared with the one by finite element method.In comparison,the bending and contact stresses of spiral bevel gears will increase as the friction increases,and the effect of friction on strength of gear under poor lubrication can not be ignored.(4)Meshing characteristic analysis of spiral bevel gears with installation errors.Finite element models of the gear with different installation errors are established based on ABAQUS,and the influence of installation errors on load distribution ratio,transmission error and bending stress of the gear are analyzed.The sensitivity of gear meshing performance to different installation errors is further investigated.It is illustrated that the meshing characteristic is significantly decreased as the installation error is negative,and the installation error exerts a great influence on the gear transmission error,whereas a little effect on bending stress. |
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